Accelerating Parallel First-Principles Excited-State Calculation by Low-Rank Approximation with K-Means Clustering

Jiang, Qingcai; Li, Jielan; Chen, Junshi; Qin, Xinming; Wan, Lingyun; Yang, Jinlong; Liu, Jie; Hu, Wei; An, Hong

doi:10.1145/3545008.3545092

Cited by 2 publications

(1 citation statement)

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“…Each cluster includes all points whose distances from the centroid of the cluster are smaller than those of other clusters. Compared to QRCP, the K-means algorithm substantially reduces both memory requirements and computational complexity. ,,,,− Since K-means clustering only converges to a local optimal solution, the accuracy of K-means clustering strongly depends on the selection of initial centroids and the definition of weight function and centroids. , …”

Section: Introductionmentioning

confidence: 99%

Machine Learning K-Means Clustering of Interpolative Separable Density Fitting Algorithm for Accurate and Efficient Cubic-Scaling Exact Exchange Plus Random Phase Approximation within Plane Waves

Zhang,

Yin,

et al. 2024

J. Chem. Theory Comput.

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The exact-exchange plus random-phase approximation (EXX+RPA) method has emerged as a crucial tool for precisely characterizing electronic structures in molecular and solid systems. We present an accurate and efficient implementation of EXX+RPA calculations that scale cubically and are conducted within plane waves. Our approach incorporates the interpolative separable density fitting (ISDF) algorithm, effectively mitigating the computational challenges associated with the plane wave basis set. To overcome the constraints of the conventional ISDF algorithm, characterized by the exceptionally high prefactor in QR factorization for interpolation point selection, we introduce an enhanced machine learning K-means method. This method incorporates a novel empirical weight function called "SSM+" for more precise interpolation point selection, capturing physical information more accurately across diverse systems. Our machine learning approach offers a quasiquadratic scaling alternative, effectively replacing the computationally demanding cubic-scaling QRCP algorithm in plane-wave-based EXX +RPA calculations. Furthermore, we enhance the method's capabilities by optimizing GPU acceleration using MATLAB's integrated GPU toolkit. In particular, our approach reduces the computational scaling of χ 0 from 3.80 to 2.13 and the overall computational scaling of EXX from 2.74 to 2.10. We achieve a remarkable GPU acceleration speedup of up to 35×. Regarding CPU computation time, the standard quartic-scaling method requires 22 h to compute Si 128 , while QRCP completes the calculation in only around 1 h, achieving a speedup up to 20×. However, the utilization of the K-means algorithm reduces the time to 800 s, a substantial improvement of 100× compared to the standard algorithm. By employing the K-means algorithm, the computational time for interpolative point calculation using QRCP decreases from 1 h to 1 min, resulting in a 55× speed increase. With this improved algorithm, we successfully computed the dissociation curve of H 2 and the equilibrium polyynic geometry of C 18 molecules.

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